Repetitive control

Abstract: The classical regulator problem is posed in the context of linear, time-invariant, finite-dimensional systems with deterministic disturbance and reference signals. Control action is generated by a compensator which is required to provide closed loop stability and output regulation in the face of small variations in certain system parameters. It is shown, using the geometric approach, that such a structurally stable synthesis must utilize feedback of the regulated variable, and incorporate in the feedback path a suitably reduplicated model of the dynamic structure of the disturbance and reference signals. The necessity of this control structure constitutes the Internal Model Principle. It is shown that, in the frequency domain, the purpose of the internal model is to supply closed loop transmission zeros which cancel the unstable poles of the disturbance and reference signals. Finally, the Internal Model Principle is extended to weakly nonlinear systems subjected to step disturbances and reference signals.

Abstract: A control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small-gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented by both the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one. >

Abstract: In this paper, the iterative learning control (ILC) literature published between 1998 and 2004 is categorized and discussed, extending the earlier reviews presented by two of the authors. The papers includes a general introduction to ILC and a technical description of the methodology. The selected results are reviewed, and the ILC literature is categorized into subcategories within the broader division of application-focused and theory-focused results.

Abstract: Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the ‘internal model principle’.

Abstract: This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune The method of tuning them is straightforward, maki